Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#384 ⋊ C2 |
| Sylow | C53 ⋊ #2039 |
306 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^52,c^b=cf,f^b=fg,h^b=h^52,e^c=eg,f^c=fg754 conjugacy classes — view the full character table.
| maximal subgroup of | #27271643, #27271645, #27296416, … |
| maximal normal subgroup of | #27271643, #27271645, #27296416, … |
| maximal quotient of | #27287416, #27287435, #27287440, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5734);